statistics

Statistics package for easy and efficient data manipulation with built-in Bayesian Network (Bayes Net), many mathematical functions and tools.

API Documentation

See the API Documentation for a full list of functions, classes and extension.

Usage

Numeric extension:

import 'package:statistics/statistics.dart';

void main() {
  var ns = [10, 20.0, 30];
  print('ns: $ns');

  var mean = ns.mean;
  print('mean: $mean');

  var sdv = ns.standardDeviation;
  print('sdv: $sdv');

  var squares = ns.square;
  print('squares: $squares');
}

OUTPUT:

ns: [10, 20.0, 30]
mean: 20.0
sdv: 8.16496580927726
squares: [100.0, 400.0, 900.0]

Statistics

The class Statistics, that have many pre-computed statistics, can be generated from a numeric collection:

import 'package:statistics/statistics.dart';

void main() {
  var ns = [10, 20.0, 25, 30];
  var statistics = ns.statistics;

  print('Statistics.max: ${ statistics.max }');
  print('Statistics.min: ${ statistics.min }');
  print('Statistics.mean: ${ statistics.mean }');
  print('Statistics.standardDeviation: ${ statistics.standardDeviation }');
  print('Statistics.sum: ${ statistics.sum }');
  print('Statistics.center: ${ statistics.center }');
  print('Statistics.median: ${statistics.median} -> ${statistics.medianLow} , ${statistics.medianHigh}');
  print('Statistics.squaresSum: ${ statistics.squaresSum }');

  print('Statistics: $statistics');
}

OUTPUT:

Statistics.max: 30
Statistics.min: 10
Statistics.mean: 21.25
Statistics.standardDeviation: 7.39509972887452
Statistics.sum: 85.0
Statistics.center: 25
Statistics.median: 22.5 -> 20.0 , 25
Statistics.squaresSum: 2025.0
Statistics: {~21.25 +-7.3950 [10..(25)..30] #4}

Bayesian Network

Bayesian Network, also known as Bayes Network, is a very important tool in understanding the dependency among events and assigning probabilities to them.

Here's an example of how to build a BayesianNetwork.

import 'package:statistics/statistics.dart';

void main(){
  var bayesNet = BayesianNetwork('cancer');

  // C (cancer) = T (true) ; F (false)
  bayesNet.addVariable("C", [
    'F',
    'T',
  ], [], [
    "C = F: 0.99",
    "C = T: 0.01",
  ]);

  // X (exam) = P (positive) ; N (negative)
  bayesNet.addVariable("X", [
    '+P',
    '-N',
  ], [
    "C"
  ], [
    "X = N, C = F: 0.91",
    "X = P, C = F: 0.09",
    "X = N, C = T: 0.10",
    "X = P, C = T: 0.90",
  ]);

  // Show the network nodes and probabilities:
  print(bayesNet);

  var analyser = bayesNet.analyser;

  // Ask the probability to have cancer with a positive exame (X = P): 
  var answer1 = analyser.ask('P(c|x)');
  print(answer1); // P(c|x) -> C = T | X = P -> 0.09174311926605506 (0.009000000000000001) >> 917.43%

  // Ask the probability to have cancer with a negative exame (X = N):
  var answer2 = analyser.ask('P(c|-x)');
  print(answer2); // P(c|-x) -> C = T | X = N -> 0.0011087703736556158 (0.001) >> 11.09%
}

Variable Dependency

To support variables dependencies you can use the method addDependency:

import 'package:statistics/statistics.dart';

void main() {
  // ** Note that this example is NOT USING REAL probabilities for Cancer!
  
  var bayesNet = BayesianNetwork('cancer');

  // C (cancer) = T (true) ; F (false)
  bayesNet.addVariable("C", [
    'F',
    'T',
  ], [], [
    "C = F: 0.99",
    "C = T: 0.01",
  ]);

  // X (exam) = P (positive) ; N (negative)
  bayesNet.addVariable("X", [
    '+P',
    '-N',
  ], [
    "C"
  ], [
    "X = N, C = F: 0.91",
    "X = P, C = F: 0.09",
    "X = N, C = T: 0.10",
    "X = P, C = T: 0.90",
  ]);

  // D (Doctor diagnosis) = P (positive) ; N (negative)
  bayesNet.addVariable("D", [
    '+P',
    '-N',
  ], [
    "C"
  ], [
    "D = N, C = F: 0.99",
    "D = P, C = F: 0.01",
    "D = N, C = T: 0.75",
    "D = P, C = T: 0.25",
  ]);

  // Add dependency between D (Doctor diagnosis) and X (Exam),
  // where the probability of a correct diagnosis is improved:
  bayesNet.addDependency([
    'D',
    'X'
  ], [
    "D = N, X = N, C = F: 0.364",
    "D = P, X = N, C = F: 0.546",
    "D = N, X = P, C = F: 0.036",
    "D = P, X = P, C = F: 0.054",

    "D = N, X = N, C = T: 0.025",
    "D = N, X = P, C = T: 0.075",
    "D = P, X = N, C = T: 0.225",
    "D = P, X = P, C = T: 0.675",
  ]);

  // Show the network nodes and probabilities:
  print(bayesNet);

  var analyser = bayesNet.analyser;
  
  // Ask the probability to have cancer with a positive exame (X = P):
  var answer1 = analyser.ask('P(c|x)');
  print(answer1); // P(c|x) -> C = T | X = P -> 0.09174311926605506 (0.009000000000000001) >> 917.43%

  // Ask the probability to have cancer with a negative exame (X = N):
  var answer2 = analyser.ask('P(c|-x)');
  print(answer2); // P(c|-x) -> C = T | X = N -> 0.0011087703736556158 (0.001) >> 11.09%

  // Ask the probability to have cancer with a positive diagnosis from the Doctor (D = P):
  var answer3 = analyser.ask('P(c|d)');
  print(answer3); // P(c|d) -> C = T | D = P -> 0.20161290322580644 (0.0025) >> 2016.13%

  // Ask the probability to have cancer with a negative diagnosis from the Doctor (D = N):
  var answer4 = analyser.ask('P(c|-d)');
  print(answer4); // P(c|-d) -> C = T | D = N -> 0.007594167679222358 (0.0075) >> 75.94%

  // Ask the probability to have cancer with a positive diagnosis from the Doctor and a positive exame (D = P, X = P):
  var answer5 = analyser.ask('P(c|d,x)');
  print(answer5); // P(c|d,x) -> C = T | D = P, X = P -> 0.11210762331838567 (0.006750000000000001) >> 1121.08%

  // Ask the probability to have cancer with a negative diagnosis from the Doctor and a negative exame (D = N, X = N):
  var answer6 = analyser.ask('P(c|-d,-x)');
  print(answer6); // P(c|-d,-x) -> C = T | D = N, X = N -> 0.0006932697373894235 (0.00025) >> 6.93%
}

See a full example for Bayes Net with Variable Dependency at GitHub:

Event Monitoring

To help to generate the probabilities you can use the BayesEventMonitor class and then build the BayesianNetwork:

import 'package:statistics/statistics.dart';

void main() {
  // Monitor events to then build a Bayesian Network:
  // ** Note that this example is NOT USING REAL probabilities for Cancer!
  var eventMonitor = BayesEventMonitor('cancer');

  // The prevalence of Cancer in the population:
  // - 1% (10:990):

  for (var i = 0; i < 990; ++i) {
    eventMonitor.notifyEvent(['CANCER=false']);
  }

  for (var i = 0; i < 10; ++i) {
    eventMonitor.notifyEvent(['CANCER=true']);
  }

  // The Exam performance when the person have cancer:
  // - 90% Sensitivity.
  // - 10% false negative (1:9).

  for (var i = 0; i < 9; ++i) {
    eventMonitor.notifyEvent(['EXAM=positive', 'CANCER=true']);
  }

  for (var i = 0; i < 1; ++i) {
    eventMonitor.notifyEvent(['EXAM=negative', 'CANCER=true']);
  }

  // The Exam performance when the person doesn't have cancer:
  // - 91% Specificity
  // - 9% false positive (89:901).

  for (var i = 0; i < 901; ++i) {
    eventMonitor.notifyEvent(['EXAM=negative', 'CANCER=false']);
  }
  for (var i = 0; i < 89; ++i) {
    eventMonitor.notifyEvent(['EXAM=positive', 'CANCER=false']);
  }

  var bayesNet = eventMonitor.buildBayesianNetwork();

  var analyser = bayesNet.analyser;

  var answer1 = analyser.ask('P(cancer)');
  print('- Cancer probability without an Exam:');
  print('  $answer1'); // P(cancer) -> CANCER = TRUE |  -> 0.01 >> 100.00%

  var answer2 = analyser.ask('P(cancer|exam)');
  print('- Cancer probability with a positive Exam:');
  print('  $answer2'); // P(cancer|exam) -> CANCER = TRUE | EXAM = POSITIVE -> 0.09183673469387756 (0.009000000000000001) >> 918.37%
}

See a full example for Bayes Net at GitHub:

CSV

To generate a [CSV][csv_wikipedia] document, just use the extension generateCSV in your data collection. You can pass the parameter separator to change the value separator (default: ,).